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Length of Summit Curve Given Angle Grades Formula

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Length of Curve is the distance along the road where the alignment changes from upward to downward slope, creating a valley-shaped concave. Check FAQs

L s = S \cdot 2 + \frac{h 1}{n 1} + \frac{h 2}{n 2}

L_s - Length of Curve?S - Sight Distance?h₁ - Driver Sight Height?n₁ - Positive Grade Angle?h₂ - The Height of The Obstruction?n₂ - Negative Grade Angle?

Length of Summit Curve Given Angle Grades Example

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Here is how the Length of Summit Curve Given Angle Grades equation looks like with Values.

Here is how the Length of Summit Curve Given Angle Grades equation looks like with Units.

Here is how the Length of Summit Curve Given Angle Grades equation looks like.

8.0669 = 3.56 \cdot 2 + \frac{0.75}{45} + \frac{0.36}{-45}

8.0669m = 3.56m \cdot 2 + \frac{0.75m}{45°} + \frac{0.36m}{-45}

8.0669 = 3.56 \cdot 2 + \frac{0.75}{45} + \frac{0.36}{-45}

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Length of Summit Curve Given Angle Grades Solution

Follow our step by step solution on how to calculate Length of Summit Curve Given Angle Grades?

FIRST Step Consider the formula

L s = S \cdot 2 + \frac{h 1}{n 1} + \frac{h 2}{n 2}

Next Step Substitute values of Variables

∴

L s = 3.56m \cdot 2 + \frac{0.75m}{45°} + \frac{0.36m}{-45}

Next Step Convert Units

∴

L s = 3.56m \cdot 2 + \frac{0.75m}{0.7854rad} + \frac{0.36m}{-45}

Next Step Prepare to Evaluate

∴

L s = 3.56 \cdot 2 + \frac{0.75}{0.7854} + \frac{0.36}{-45}

Next Step Evaluate

∴

L s = 8.06692965855155m

LAST Step Rounding Answer

∴

L s = 8.0669m

Length of Summit Curve Given Angle Grades Formula Elements

Variables

Length of Curve

Length of Curve is the distance along the road where the alignment changes from upward to downward slope, creating a valley-shaped concave.

Symbol: L_s

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Length of Curve

Sight Distance

Sight Distance is s the minimum distance between two vehicles moving along a curve, when the driver of one vehicle can just see the other vehicle on the road.

Symbol: S

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Sight Distance

Driver Sight Height

Driver Sight Height refers to the vertical distance between the driver's eye level and the road surface while seated in a vehicle.

Symbol: h₁

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Driver Sight Height

Positive Grade Angle

A positive grade angle indicates an upward slope.

Symbol: n₁

Measurement: AngleUnit: °

Note: Value should be greater than 0.

Formulas to find Positive Grade Angle

The Height of The Obstruction

The Height of The Obstruction refers to its vertical dimension, blocking a line of sight or path, often in transportation, construction or safety.

Symbol: h₂

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find The Height of The Obstruction

Negative Grade Angle

A negative grade angle indicates an incline slope.

Symbol: n₂

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Negative Grade Angle

Other formulas in Length of Summit Curve with Grade Angles category

Go Height of Obstruction Given Angle Grades

h 2 = (S - \frac{L s}{2} - \frac{h 1}{n 1}) \cdot n 2

Go Driver Sight Height given Angle Grades

h 1 = \frac{L s}{2} + S \cdot n 1 + \frac{h 2}{n 2}

Go Negative Grade Angle Given Sight Distance

n 2 = \frac{h 2}{S - \frac{L s}{2} - \frac{h 1}{n 1}}

Go Positive Grade Angle Given Sight Distance

n 1 = \frac{h 1}{S - \frac{L s}{2} - \frac{h 2}{n 2}}

How to Evaluate Length of Summit Curve Given Angle Grades?

Length of Summit Curve Given Angle Grades evaluator uses Length of Curve = Sight Distance*2+Driver Sight Height/Positive Grade Angle+The Height of The Obstruction/Negative Grade Angle to evaluate the Length of Curve, The Length of Summit Curve Given Angle Grades formula is determined by doubling the sight distance, then adding the driver's eye height divided by the positive grade angle and the height of the obstruction divided by the negative grade angle. Length of Curve is denoted by L_s symbol.

How to evaluate Length of Summit Curve Given Angle Grades using this online evaluator? To use this online evaluator for Length of Summit Curve Given Angle Grades, enter Sight Distance (S), Driver Sight Height (h₁), Positive Grade Angle (n₁), The Height of The Obstruction (h₂) & Negative Grade Angle (n₂) and hit the calculate button.

FAQs on Length of Summit Curve Given Angle Grades

What is the formula to find Length of Summit Curve Given Angle Grades?

The formula of Length of Summit Curve Given Angle Grades is expressed as Length of Curve = Sight Distance*2+Driver Sight Height/Positive Grade Angle+The Height of The Obstruction/Negative Grade Angle. Here is an example- 8.06693 = 3.56*2+0.75/0.785398163397301+0.36/(-45).

How to calculate Length of Summit Curve Given Angle Grades?

With Sight Distance (S), Driver Sight Height (h₁), Positive Grade Angle (n₁), The Height of The Obstruction (h₂) & Negative Grade Angle (n₂) we can find Length of Summit Curve Given Angle Grades using the formula - Length of Curve = Sight Distance*2+Driver Sight Height/Positive Grade Angle+The Height of The Obstruction/Negative Grade Angle.

Can the Length of Summit Curve Given Angle Grades be negative?

No, the Length of Summit Curve Given Angle Grades, measured in Length cannot be negative.

Which unit is used to measure Length of Summit Curve Given Angle Grades?

Length of Summit Curve Given Angle Grades is usually measured using the Meter[m] for Length. Millimeter[m], Kilometer[m], Decimeter[m] are the few other units in which Length of Summit Curve Given Angle Grades can be measured.

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Length of Summit Curve Given Angle Grades Formula

Length of Summit Curve Given Angle Grades Example

Length of Summit Curve Given Angle Grades Solution

Length of Summit Curve Given Angle Grades Formula Elements

Other formulas in Length of Summit Curve with Grade Angles category

How to Evaluate Length of Summit Curve Given Angle Grades?

FAQs on Length of Summit Curve Given Angle Grades

Variable Name